Question

A monopolist’s demand curve is given by P = 100 – 2q.
(a) Find his marginal revenue function.
(b) At what price is marginal revenue zero?

Answer 1

Demand curve is given by
P = 100 - 2q
Total revenue will be given by
TR = P×q = (100-2q)×q = 100q - 2q²

(a) marginal revenue is the derivative of TR. So

$MR= \frac{d(TR)}{dq} = \frac{d}{dq}(100q-2q^2) =100-4q$

So marginal revenue is 100-4q. 

(b) MR = 0
⇒ 100 - 4q = 0
⇒ 4q = 100
⇒ q = 100/4 = 25

At q=25, 
TR =  100q - 2q²
     = 100×25 - 2×25²
     = 2500 - 1250
     = 1250
Marginal Revenue is 0 at Price 1250.

Answer 2

Answer:

o marginal revenue is 100-4q. Marginal Revenue is 0 at Price 1250.